Quadric Surfaces

Ellipse

import sympy as sp
import spb 
from spb import PB
from math import pi

u, v = sp.symbols("u, v")
a, b, c = 1, 1, 1

r = 2 + sp.sin(7 * u + 5 * v)
expr = (
    a * sp.cos(u) * sp.sin(v),
    b * sp.sin(u) * sp.sin(v),
    c * sp.cos(v)
)

spb.plot3d_parametric_surface(*expr, (u, 0, 2 * sp.pi), (v, 0, sp.pi), "expr", backend=PB, use_cm=True)

<spb.backends.plotly.plotly.PlotlyBackend at 0x150e363fe850>

import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots

# Function to generate ellipsoid points
def generate_ellipsoid(a, b, c, num_points=100):
    u = np.linspace(0, 2 * np.pi, num_points)
    v = np.linspace(0, np.pi, num_points)
    x = a * np.outer(np.cos(u), np.sin(v))
    y = b * np.outer(np.sin(u), np.sin(v))
    z = c * np.outer(np.ones(np.size(u)), np.cos(v))
    return x, y, z

# Initial parameters
a, b, c = 1, 1, 1

# Generate initial ellipsoid points
x, y, z = generate_ellipsoid(a, b, c)

# Create the figure
fig = make_subplots(rows=1, cols=1, specs=[[{'type': 'surface'}]])

# Add the initial ellipsoid
fig.add_trace(go.Surface(x=x, y=y, z=z, colorscale='Viridis', showscale=False))

# Set fixed axis limits and aspect ratio
fig.update_layout(
    title=f'Ellipsoid: a={a}, b={b}, c={c}',
    scene=dict(
        xaxis_title='X',
        yaxis_title='Y',
        zaxis_title='Z',
        xaxis=dict(range=[-3, 3]),
        yaxis=dict(range=[-3, 3]),
        zaxis=dict(range=[-3, 3]),
        aspectmode='cube'  # Fix aspect ratio
    )
)

# Create sliders for semi-major axes a, b, and c
fig.update_layout(
    sliders=[
        {
            'active': 0,
            'yanchor': 'top',
            'xanchor': 'left',
            'currentvalue': {
                'prefix': 'Semi-Major Axis a: ',
                'visible': True,
                'xanchor': 'right'
            },
            'pad': {'b': 10},
            'len': 0.9,
            'x': 0.1,
            'y': -0.1,
            'steps': [{
                'label': f'{i/10:.1f}',
                'method': 'update',
                'args': [{'x': [generate_ellipsoid(i/10, b, c)[0]], 
                             'y': [generate_ellipsoid(i/10, b, c)[1]], 
                             'z': [generate_ellipsoid(i/10, b, c)[2]]},
                          {'title': f'Ellipsoid: a={i/10:.1f}, b={b}, c={c}'}]
                } for i in range(1, 21)]  # Steps for semi-major axis a
        },
        {
            'active': 0,
            'yanchor': 'top',
            'xanchor': 'left',
            'currentvalue': {
                'prefix': 'Semi-Major Axis b: ',
                'visible': True,
                'xanchor': 'right'
            },
            'pad': {'b': 10},
            'len': 0.9,
            'x': 0.1,
            'y': -0.3,
            'steps': [{
                'label': f'{i/10:.1f}',
                'method': 'update',
                'args': [{'x': [generate_ellipsoid(a, i/10, c)[0]], 
                             'y': [generate_ellipsoid(a, i/10, c)[1]], 
                             'z': [generate_ellipsoid(a, i/10, c)[2]]},
                          {'title': f'Ellipsoid: a={a}, b={i/10:.1f}, c={c}'}]
                } for i in range(1, 21)]  # Steps for semi-major axis b
        },
        {
            'active': 0,
            'yanchor': 'top',
            'xanchor': 'left',
            'currentvalue': {
                'prefix': 'Semi-Major Axis c: ',
                'visible': True,
                'xanchor': 'right'
            },
            'pad': {'b': 10},
            'len': 0.9,
            'x': 0.1,
            'y': -0.5,
            'steps': [{
                'label': f'{i/10:.1f}',
                'method': 'update',
                'args': [{'x': [generate_ellipsoid(a, b, i/10)[0]], 
                             'y': [generate_ellipsoid(a, b, i/10)[1]], 
                             'z': [generate_ellipsoid(a, b, i/10)[2]]},
                          {'title': f'Ellipsoid: a={a}, b={b}, c={i/10:.1f}'}]
                } for i in range(1, 21)]  # Steps for semi-major axis c
        }
    ]
)

# Show the figure
fig.show()